The light has a timer switch to turn off after a short time (3 minutes or so). I believe the fuse is rated at 5 amp to protect this switch. Specifically it is called a Smart Highside High Current Switch, model DTM904, supplied by KIB electronics in Elkhart.
Link to vendor information. Looks like the ones used for door timers might be customized - I'm not sure though, as mine is labeled DTM904-2.
Here is a pic of mine.
I would stay with the 5 amp even though the circuit may be "generically labelled" for 15amp (labelling can be incorrect). The info from KIB does show their current model is limited to max of 12amp. I would be comfortable putting a 10amp in mine. I beleive though my fuse is a 5 amp as well, even though its label shows 15 amp like yours.
Hope this helps.
Brian